5.13 Consider the data set containing quarterly U.S. unemployment, U.S. GNP, consumption, and government and private investment from 1948-III to 1988-II. The seasonal component has been removed from the data. Concentrating on unemployment (Ut), GNP (Gt), and consumption (Ct), fit a vector ARMA model to the data after first logging each series, and then removing the linear trend. That is, fit a vector ARMA model to xt = (x1t, x2t, x3t), where, for example, x1t = log(Ut) − β0 − β1t, where

β0 and β1 are the least squares estimates for the regression of log(Ut) on time, t. Run a complete set of diagnostics on the residuals.